Sunday, July 30, 2006

Sunday Morning Geometry

I studied Mobius geometries in the extended complex plane this morning. I enjoy getting my mind around some mathematics every now and then. Any mathematics will do, whether just right, too difficult, or too easy. The difficult sometimes resolves itself into the obvious and the obvious often exposes unexpected difficulties upon reflection.

I view mathematics as art and imagination. It’s all of a piece with poetry, painting, sculpture, architecture, music, and such. I must write down what I mean by that someday.

2 Comments:

At 7:34 PM, Blogger janus said...

I studied Mobius geometries in the extended complex plane this morning.

oddly enough, so did i .. more accurately, it was in the afternoon.

odder still, i was trying to "de-complex" the discussion. mobius transformations do make sense in higher dimensions, but they are nowhere as pleasant-looking as in the complex plane. pity, that.

 
At 1:19 AM, Blogger Lynn said...

janus-

I can work out the arithmetic (vary laboriously), but the intuition has me scuffling at times. I'd rather have the intuition first and the arithmetic second. But that is not my fate.

Higher dimensions, other than 3, may forever be out of my grasp.

 

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